The covering relation in the lattice of subuniverses of a finite distributive lattice is characterized in terms of how new elements in a covering sublattice fit with the sublattice covered. In general, although the lattice of subuniverses of a finite distributive lattice will not be modular, nevertheless we are able to show that certain instances of Dedekind’s Transposition Principle still hold...

Mining trajectory datasets has many important applications. Real trajectory data often involve uncertainty due to inadequate sampling rates and measurement errors. For some trajectories, their precise positions cannot be recovered and the exact routes that vehicles traveled cannot be accurately reconstructed. In this paper, we investigate the uncertainty problem in trajectory data and present a...

Map Generalization is one of the hotspot issues in GIS. It is the most imperative field for intelligence in GIS. The uncertainty and data quality of map generalization should be attached importance to in map generalization. The conventional methods of process of line generalization in map generalization are be introduced in this paper, and analysis decline in the quality of integrated because o...

We examine the problem of minimizing uncertainty in the automated construction of a visual map of an unknown environment. Our work is motivated by the idea that a robot’s exploration policy can impact the accuracy of the resulting map, and we seek to examine the behavior of a set of policies that exhibit a trade-off between accuracy and efficiency. We are further motivated by the specific requi...

The authors present a detailed analysis of the asymptotic frequentist properties of credible sets derived from posteriors with normal-linear measurement models and horseshoe priors. Although we disagree with the claim that “In Bayesian practice credible balls are nevertheless used as if they were confidence sets”, the results in the paper are important for identifying where the horseshoe priors...

Recent research in robot exploration and mapping has focused on sampling hotspot fields, which often arise in environmental and ecological sensing applications. Such a hotspot field is characterized by continuous, positively skewed, spatially correlated measurements with the hotspots exhibiting extreme measurements and much higher spatial variability than the rest of the field. To map a hotspot...

This paper explores a methodology for quantifying the uncertainty of DEMs created by digitising topographic maps. The origins of uncertainty in DEM production were identified and examined. The uncertainty of DEM data was quantified by computing a vector total of Root Mean Square Error (RMSE) from the source map, sampling and measurement errors, and the interpolation process. Distributional meas...

Uncertainty in spatial data attributes can produce unreliable spatial patterns in choropleth maps, but only a few studies have considered uncertainty in map classification processes. Unfortunately, a less desirable classification result often is generated by existing methods. For example, most observations are assigned to a single class while the remaining classes have a very small number of ob...